Finite Group DatabasebetaFinite Group Databasebeta| order | 19200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 84557168640 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C27×C43 |
| abelian | C22×C3×C43×C25 |
| multiplicative | (ℤ/52520)ˣ, (ℤ/56560)ˣ, (ℤ/63024)ˣ, (ℤ/72720)ˣ, (ℤ/78000)ˣ, (ℤ/78780)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23×C5 | C25×C3×C5 |
| socle, prime radical | C25×C3×C5 | C23×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
24282 conjugacy classes of subgroups.
19200 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.